Compressing Massive Relational Data

ABSTRACT

A relational dependency transform is introduced as a way to exploit information redundancy in conditioning data in a relational database for better compressibility. An optimum relational dependency transform of the relational database is first computed. Fields of the relational database are then sorted topologically based on a weighted, directed graph having nodes representing predictor and predictee fields. For each predictee field in the topological order, a transformed field is then computed via the relationship between predictor and predictee in the optimum relational dependency transform.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationSer. No. 12/655,014, entitled “Compressing Massive Relational Data,”filed on Dec. 22, 2009, the disclosure of which is incorporated hereinby reference in its entirety.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to the compression of data in arelational database, and more particularly, to the preparation of databy exploiting type-limited field values, similar field values and fieldcorrelations to improve the performance of data compressors.

BACKGROUND

Relational data files store data in the format of records and fields.Examples of such data include transaction tables, event logs, businessreports, etc. Massive volumes of relational data are produced daily inlarge business and information systems, from gigabytes in banking andtelephone services to terabytes in IP network monitoring and managementsystems. Thus, good compression is an important component in thesesystems to manage costs.

Compression research has evolved over the years from studying onlygeneral information models to finding ways to exploit specificstructures in data. In H. Liefke and D. Suciu. Xmill: An EfficientCompressor for XML Data, In Proceedings of SIGMOD, pages 153-164 (2000),the contents of which is hereby incorporated by reference herein in itsentirety, the authors discussed how XML files could be compressed bygrouping data with the same tree paths together. Their work was inspiredby the Pzip compressor described in A. Buchsbaum, G. S. Fowler, and R.Giancarlo, Improving Table Compression with Combinatorial Optimization,J. of the ACM, 50(6):825-51 (2003) (hereinafter “Buchsbaum et al.”), thecontents of which is hereby incorporated by reference herein in itsentirety, for a special type of relational data, namely, tables ortwo-dimensional arrays of bytes. Pzip introduced the idea of fixing somegeneral purpose compressor, then grouping together columns amenable tocompress well with that compressor. A different approach to tablecompression was later introduced B. D. Vo and K.-P. Vo, CompressingTable Data with Column Dependency, Theoretical Computer Science, v. 387,pp. 273-283 (2007) (hereinafter “Vo and Vo”), the contents of which ishereby incorporated by reference herein in its entirety, byautomatically discovering certain dependency relations among tablecolumns and using that to reorder data to enhance compressibility.

The use of compression to improve database storage and access has beenwidely studied, especially along with field-oriented storage schemes.The authors of J. Goldstein, R. Ramakrishnan, and U. Shaft, CompressingRelations and Indexes, ICDE (1998), the contents of which is herebyincorporated by reference herein in its entirety, observed that fielddata are often sparse within their much larger ranges and developed aframe of reference approach to compactly code such data. In M. Poess andD. Potapov, Data Compression in Oracle, VLDB (2003), the contents ofwhich is hereby incorporated by reference herein in its entirety, theauthors discussed how the Oracle DBMS saved space by replacing commonlyoccurring field attributes by pointers to distinct instances stored insome dictionary. V. Raman and G. Swart, How to Wring a Table Dry:Entropy Compression of Relations and Querying of Compressed Relations,VLDB (2006) (hereinafter “Raman and Swart”), the contents of which ishereby incorporated by reference herein in its entirety, proposed a morecomprehensive approach to compress database tables based on exploitingvalue sparsity, field correlation and lack of record order.

The present disclosure focuses on the problem of compressing relationaldata files. Despite the apparent similarity, there are notabledifferences between compressing a database table and compressing arelational data file:

-   -   Unordered vs. Ordered: In a database table, record ordering is        immaterial as queries can return retrieved records in any order.        By contrast, the order of records in a relational data file is        often meaningful due to implicit but often unknown factors such        as time series data or categories in a presentation or report.        As such, a compressed relational data file should always        decompress into its exact original state.    -   Typed vs. Typeless: Schemas in a database specify precisely the        type of each field and the association of such fields in their        relations. However, such meta-data are often unavailable with a        relational data file. That is, little can be assumed beyond        being able to partition such a file into sequences of bytes        representing records and fields. Any further structures must be        automatically deduced.

SUMMARY OF THE DISCLOSURE

In accordance with a first aspect of the disclosure, a method isprovided for preparing a relational database R for compression by acompressor C. An optimum relational dependency transform D comprising aset of field dependency relations (p, f) is computed, wherein p is apredictor field of R and f is a predictee field of R. The fields of Rare sorting topologically based on a graph G(D), the graph G(D) having anode set that is a set of all predictor fields p and predictee fields f,and having an edge set that comprises every dependency relation (p, f)of D, each edge having a weight C(δ_(p)(f)) wherein a field f istransformed by a transform δ_(p) based on a defined permutation of thefield p, relative to the compressor C. For each field f in a resultingtopologically sorted database R, δ_(p)(f) is computed via the relation(p, f)εD.

The compressor C may be a data compressor tailored for compressing dataof types found in the fields of database R.

The step of sorting the fields of R topologically may be based on a setof field-specific orderings of values. In that case, the values in thefields may be sorted as strings of bytes, in a lexicographical order, ormay be sorted as numerical values in a numerical order.

An application may define its own ordering for sorting the values in thefields. There preferably are no cyclic sequences in D.

Another aspect of the disclosure is a computer-usable medium havingcomputer readable instructions stored thereon for execution by one ormore processors to perform methods described herein

According to yet another aspect of the disclosure, a method is providedfor compressing a relational database R using a training set of recordsand a compressor C. Using the training set of records, a relationaldependency transform D is computed by (1) computing an optimumrelational dependency transform D comprising a set of field dependencyrelations (p, f) wherein p is a predictor field of R and f is apredictee field of R; (2) sorting the fields of R topologically based ona graph G(D), the graph G(D) having a node set that is a set of allpredictor fields p and predictee fields f, and having an edge set thatcomprises every dependency relation (p, f) of D, each edge having aweight C(δ_(p)(f)) wherein a field f is transformed by a transform δ_(p)based on a defined permutation of the field p, relative to thecompressor C; and (3) for each field f in a resulting topologicallysorted database R, computing δ_(p)(f) via the relation (p, f)εD.

R is then divided into segments comprising groups of records. Using therelational dependency transform D, the fields of each segment aretransformed. Each transformed field is then compressed using thecompressor C.

These aspects of the disclosure and further advantages thereof willbecome apparent to those skilled in the art as the present disclosure isdescribed with particular reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary relational data file for illustrating the methodsand systems of the present disclosure;

FIG. 2 shows data from the relational data file of FIG. 1 afterperforming a dependency field transformation according to the presentdisclosure;

FIG. 3 is a table showing compression sizes and compression ratios forcomparing various techniques including the techniques according to thepresent disclosure;

FIG. 4 is a table showing compression and decompression times in secondsfor comparing various techniques including the techniques according tothe present disclosure; and

FIG. 5 is a schematic of an exemplary computer system that can be usedto implement the techniques according to the present disclosure.

DETAILED DESCRIPTION

In the present disclosure, the relational dependency transform isdiscussed. The relational dependency transform is a function to improvethe compressibility of a relational data file by reordering its fieldvalues in an invertible way. Such a transform is a set of fielddependency relations with strengths given by conditional compressiveentropy, an information metric suitable for estimating the informationcontent in a field as well as across fields. Experimental results basedon large datasets taken from real information systems are presented toshow the effectiveness of this compression approach.

Embodiments of the disclosure will be described with reference to theaccompanying drawing figures wherein like numbers represent likeelements throughout. Before embodiments of the disclosure are explainedin detail, it is to be understood that the disclosure is not to belimited in its application to the details of the examples set forth inthe following description and/or illustrated in the figures. Thedisclosure is capable of other embodiments and of being practiced orcarried out in a variety of applications. Also, it is to be understoodthat the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having” and variations thereof herein ismeant to encompass the items listed thereafter and equivalents thereofas well as additional items.

Relational Data Files

A relational data file R is a byte sequence composing a sequence ofrecords (r₀, r₁, . . . , r_(n-1)). In turn, each record r_(i) iscomposed of a sequence of fields (f₀, f₁, . . . , f_(n-1)). Thus, R canbe thought of as a two-dimensional array whose elements are bytestrings.

A relational data file is assumed to be in record-major order. That is,data are stored record by record with fields from left to right in eachrecord. There are generally two main formats for field data, binary withfixed field lengths, or textual with fields separated by some separator.All examples in this disclosure will be based on the text format.

Unless noted otherwise in the disclosure, the field f indicates thecolumn R[f] of the relational data file R when considered as a twodimensional array. By abusing notation, f is also used to denote thebyte string formed by concatenating all values in field f together.

FIG. 1 depicts an example relational data file 100 that stores customerbeer purchases. This example relational data file will be usedthroughout the present disclosure to illustrate the presented conceptsand methods. The top portion 105 of the file shows eight records, eachincluding five colon-separated fields: Name, Phone, Date, Amount, andBeer.

Those textual data records could have been externalized forms of binaryinstances of the C language structure shown in the lower portion 106 ofthe file. If the structure data were output verbatim, field values wouldbe byte strings with fixed lengths. For example, the Name field wouldhave length 20 while the integer field Amount would have length 4 on a32-bit machine.

Dependency Transforms

All compression methods aim at reducing redundancy in theinformation-theoretic content of given data. Three of the more commonsources of redundancy in relational data files are type-limited fieldvalues, similar field values and field correlations. They are discussedin the following paragraphs.

Type-limited field values: Field values are byte strings so there couldbe up to 256^(k) different occurrences for a value of length k. However,in practice, the number of possible representations will be small due totype limitation. For example, the Amount field in the example relationaldata file 100 stores only small integers, so a value represented as astring of length k would have range size 10^(k) instead of 256^(k). Thechallenge in compression is to take advantage of this phenomenon withoutany a priori knowledge of field types.

Similar field values: Many values in a relational data file are distinctyet similar. For example, the Name field in the example file 100 shows“Leno, J.” and “Leno, K.” as two names with the same phone numbers. Thiscould be different people in the same household or a typographicalerror. Knowing which is which might be an important data processingissue. But, from a data compression point of view, the main significanceis that the similarity of the strings can be exploited to enhancecompressibility.

Field correlations: Values in different fields may correlate with oneanother; e.g., the Name and Phone fields in the running example file100. Such field correlations represent information redundancy that canbe factored out in compression. As seen with the Leno records, thiseffect can be strong when approximately matched data are considered.

Next is developed the idea of a relational dependency transform toexploit the above features for compression. The discussion is related tothat of the k-transform by Vo and Vo for table compression. However, thepresently-described transform is designed to work on complex fields, notcolumns of single bytes. First, the field transform is defined:

Definition 1. Let R be a relational data file with m fields and nrecords. A dependency relation is a pair of fields (p, f). Let π_(p) bethe unique permutation that sorts the rows of field p lexicographicallyand stably. The field transform δ_(p) is defined byδ_(p)(f)[k]=f[π_(p)[k]] for 0≦k<n.

In a dependency relation (p, f), p is called the predictor and f thepredictee. The π_(p) permutation is called a transform vector. It isclear that, as long asp is available, a transformed field δ_(p)(f) canbe inverted via f[π_(p)[k]]=δ_(p)(f)[k] for 0≦k<n.

It is noted that the use of a stable and lexicographic sort method isjust one way to define π_(p). Any method to produce a well-definedpermutation by grouping data can be used, as applicable. In the generalcase, an application may use any standard or specially-devised semanticsof a field to order its values. For example, if the values in a fieldare numerical values, the field-specific application-defined order maybe a numerical order. In another example, if a field contains 32-bit IPaddresses of the form 1.23.45.67, the application might treat eachcomponent of the four components as a numerical value, and then sort theentire set of IP addresses by their 4-value strings in a lexicographicorder. Other application-defined orders of values may be used.

It is useful to consider dependency relations of the form (φ, f), whereφ is a virtual field and f a real field. The associated transform vectorπ_(φ) is defined to be the identity permutation so that δ_(φ)(f)=f.

A practical way is needed to measure the information content of astring. Following Buchsbaum et al., a compressor C is fixed and thecompressive entropy of a byte string s is defined relative to C as|C(s)|, the length of the data after being compressed by C. The measureof information content across fields can now be defined as follows:

Definition 2. Let R be a relational data file and C some datacompressor. If (p, f) is a dependency relation, the conditionalcompressive entropy of field f given field p is defined as|C(δ_(p)(f))|.

Note that, for any field f, |C(f)=|C(δ_(φ)(f))|, so compressive entropyis a special case of conditional compressive entropy. |C(f)|<|f| meansthat the information content of field f is less than its raw data. Suchan indication of information sparsity might be due to the field havingfew distinct values or because its values have similar characteristics.

More interestingly, |C(δ_(p)(f))|<|C(f)| means that field f can becompressed better after being transformed by δ_(p). From an informationperspective, this means that the content of f is largely predictable byp. That is, the two fields are not independent from one another.

FIG. 2 shows the fields Name and Phone and their data 200 after beingtransformed by one another. The top portion 205 shows the record indexesand the fields in their original order. The first column of the bottomportion 206 shows the transform vector π_(Name), the permutation of theindexes of the Name field after being lexicographically and stablysorted. π_(Phone) is the same as π_(Name) by construction. The secondcolumn in the bottom portion 206 shows the Phone field after beingtransformed by δ_(Name). Likewise, in the third column is the Name fieldafter being transformed by δ_(Phone).

Suppose that compressor C codes runs of same values. Then,|C(δ_(Name)(Phone))|<|C(Phone)| because the transformed field Phonecould be coded with 4 runs while the original must be coded with 7 runs.|C(δ_(Phone)(Name)|<|C(Name)| for similar reasons. As such, both Nameand Phone are good transforms to enhance compression per compressor C.However, δ_(Name) would be better than δ_(Phone) because|C(δ_(Name)(Phone))|<|C(δ_(Phone)(Name)|.

A sequence of field transforms used in compression must be carefullychosen so that the transformed data can be decompressed. Thus, in theabove example, only one of the transforms δ_(Name) or δ_(Phone) could beused. That is because when one of the fields is reconstructed duringdecompression, the other must be already in its original form for itscorresponding transform vector to be computable. In general, cyclicsequences of relations must be avoided. This leads to the followingdefinition:

Definition 3. Let R be a relational data file and D be a set of fielddependency relations. Then, D is said to be a relational dependencytransform if:

Every field f is a predictee in exactly one dependency relation (p,f)εD, and

There is no sequence (p₁, f₁), . . . , (p_(k), f_(k)) in D such thatp₁=f_(k).

For any set S of dependency relations, a weighted directed graph G(S)can be constructed by letting the node set be the set of predictors andpredictees and the edge set comprises every pair (p, f)εD with weightC(δ_(p)(f)). In addition, let the compressive size of S be defined asΣ_((p, f)εS)|C(δ_(p)(f))|.

As the focus is in compressing massive data, only linear-time algorithmsare of interest for the choice of the compressor C used for computingcompressive entropy. The below result therefore follows for thecomplexity of computing an optimum relational dependency transform:

Theorem 1. Let R be a relational data file with m fields and n recordswhere m≦n and C a linear-time compressor. Then, an optimum relationaldependency transform D, i.e., one with smallest compressive size, can becomputed in time O(m|R|).

Proof. Let E be the set of all dependency relations (p, f) where f is areal field of R while p≠f can be either a real field or φ, the virtualfield. If D is a relational dependency transform for R then D is asubset of E. Now, consider the graphs G(E) and G(D). By definition,every field f is in exactly one dependency relation (p, f)εD. Sincethere is no cyclic sequence of relations, the graph G(D) must form abranching in G(E), as shown by J. Edmonds, Optimum Branchings, J. ofRes. of The National Bureau of Standards, 71B:233-240 (1967), thecontents of which is hereby incorporated by reference herein in itsentirety.

Thus, computing an optimum relational dependency transform for the fileR is equivalent to computing an optimum branching in G(E). Theoptimum-branching algorithm set forth in T. Spencer H. N. Gabow, Z.Galil and R. E. Tarjan, Efficient Algorithms for Finding MinimumSpanning Trees in Undirected and Directed Graphs, In Proc. 25th AnnualIEEE Symp. on Found. of Comp. Sci., pages 347-357 (1984), the contentsof which is hereby incorporated by reference herein in its entirety,solves this problem in time O((m+1)log(i+1)+m(m+1)/2) because G(E) hasm+1 nodes and m(m+1) edges. With n>m, the time can be bounded by O(mn).

To quantify the total cost to compute an optimum dependency transform D,the cost to construct G(E) must also be estimated. The cost ofconstructing an edge from p to f is O(|f|+n) since the reordering ofvalues off by δ_(p) costs O(n) while compressing the result with C costsO(|f|) by the assumption that C runs in linear time. As every field fhas m possible predictors, the cost to construct all edges with f as apredictee is O(m(|f|+n)). Summing this quantity over all fields yieldsO(m²n+mΣ_(f)|f|)=O(m²n+m|R|).

So, the total cost to compute an optimum dependency transform isO(m²n+m|R|+mn) with mn being the cost of computing the optimumbranching. Since mn≦|R|, the expression simplifies to O(m|R|).

The condition m≦n in the theorem was just a formality. Any practicalrelational data file would have far more records than fields becausefields represent abstract objects while records store actual instancesof these objects and their relationships. In fact, in most cases, thenumber of fields would be small enough to be considered a constant.Then, the time to compute an optimum relational data transform can beseen as linear in the size of the data.

The following is a method RDT(R) to transform a relational data file R:

RDT(R)

1. Compute an optimum relational dependency transform D.

2. Sort the fields of R topologically based on G(D).

3. For each field f in this topological order, compute p(f) via theunique relation (p, f)εD.

First, an optimum relational dependency transform D is computed at acost O(m|R|) time. Topologically sorting the fields takes time O(m)where m is the number of fields. Finally, reordering the values in thefields cost O(|R|). Thus, the total running time for the method isO(m|R|). This theorem follows:

Theorem 2. Let R be a relational data file with m fields and n recordswhere m≦n and C a linear-time compressor. Then, RDT transforms R in timeO(m|R|).

Inverting RDT is straightforward. Each field f is separately inverted inthe same topological order shown in step 2 of the above method RDT. Thetopological order ensures that before the values of a field f are to beinverted the unique predictor p of f would be available in its originalform. Thus, any needed transform vector will always be well-defined.

The major cost to invert RDT is in computing the transform vectors. Aseach is computed once per field f and costs O(|f|) using bucket sort,the entire inversion process costs O(|R|). Therefore:

Theorem 3. Let R be any relational data file. The transformed dataRDT(R) can be inverted in time O(|R|).

Compression Strategy

Below are a few engineering considerations in building and running acompressor:

-   -   Method RDT often yields the same optimum dependency transform        when different compressors are used to compute compressive        entropy. This is used to advantage by emulating a fast        compressor that simply factors matched prefixes of successive        field values to calculate compressive entropy without actually        compressing.    -   Any compressor could be used to compress field data since they        are just strings of bytes. The compressor may be an        application-defined data compressor tailored to the types of        data in the fields. The example of the present disclosure uses        the Vo and Vo table compressor. Since it deals with fixed-length        field data, fields with variable lengths are padded to a uniform        length.    -   It is often not possible to process all of a large file in        memory; nor is it necessary. In the present disclosure, the data        is divided into windows; i.e., horizontal segments with suitable        sizes, to be processed entirely in core each at a time. By        default, the presently described compressor counts enough        records to make up about 8 MBs and uses that as a window of data        for compression.    -   Records in a relational data file tend to have similar        characteristics. Thus, a sample of a few thousand records is        more than adequate to compute an optimum dependency transform.        Further, a computed transform can be reused in all windows of        data.

The following is a compression scheme Compress(R) based on relationaldata transformation and the above engineering considerations:

Compress(R)

1. Use a training set of records to compute a relational dependencytransform D.

2. Divide R into horizontal segments of appropriate sizes.

3. Transform field data in each segment via D.

4. Compress each transformed field based on some selected compressor C.

The time cost for the first three steps is bounded by O(|R|) becauseonly a small amount of data is used to compute D. Thus, the dominanttime cost is incurred by the chosen compressor C. For example, if C is alinear time algorithm, then the entire compression process would run inlinear time.

Performance

The experimental data presented here were obtained on a PC runningUbuntu Linux over a Pentium Conroe E2200 CPU with 2Gs of RAM.

The first two test compressors below were standard tools chosen toprovide baseline data on how well compression could be done without anyknowledge of structures in data. The last three helped to contrastcompression results between using relational dependency transforms andnot.

-   -   Gzip: the Unix compressor based on compression techniques        described in J. Ziv and A. Lempel, A Universal Algorithm for        Sequential Data Compression, IEEE Transactions on Information        Theory, 23(3):337-343 (May 1977), and in D. A. Huffman, A Method        for the Construction of Minimum-Redundancy Codes, Proceedings of        the IRE, 40(9):1098-1101 (September 1952).    -   Bzip: a compressor described in J. Seward, Bzip2,        http://www.bzip.org. Technical report (1994), and based on the        Burrows-Wheeler Tranform (BWT) set forth in M. Burrows and D. J.        Wheeler, A Block-Sorting Lossless Data Compression Algorithm,        Report 124, Digital Systems Research Center (1994).    -   FIELD: a compressor based on padding field data to same lengths,        then applying the table compressor described by Vo and Vo to        each field.    -   TABLE: a compressor based on padding field data to same lengths,        then treating the entire data as a large table and applying the        Vo and Vo table compressor.    -   RDT: a compressor based on first transforming data with a        relational dependency transform, padding fields as above, then        applying the Vo and Vo table compressor to each transformed        field.

The below test datasets were selected to represent broad categories ofdata including population statistics, finance, and computer and networkengineering.

v9mpls: Samples of router to router connections in a large IP network.

-   -   stats: Performance statistics of components in a computing        platform.    -   ca00003_uf1: A subset of the 2000 US Census data for California.    -   flow: Sample statistics of flows through various peer-to-peer        networks.    -   ihrwpxco: Sample billing records of telephone calls fully rated        for costs and taxes.

FIG. 3 presents a table 300 showing the raw and compressed sizes ofdata. The second row in each box for a compressor shows the respectivecompression ratio. Here are some observations:

-   -   RDT compressed best overall. Both TABLE and RDT did well as they        were able to take advantage of dependency across fields to        rearrange data. FIELD also did well even though it lost to Bzip        on ca00003_uf1. This file had many fields of small integers and        Bzip was able to pick up some dependency relations across fields        due to its use of the Burrows-Wheeler Transform for context        sorting. Gzip was far worse than the other compressors in all        cases.    -   RDT improved substantially over FIELD as expected. The table        compressor of Vo and Vo uses column dependency relations to        rearrange data. Such relations, however, would be rare among        columns of a single field, especially if such a field does not        possess some complex substructure. The relational dependency        transforms based on field dependency had larger contexts to work        with and were much more effective than FIELD at rearranging data        for compressibility.    -   The improvement of RDT over TABLE was noteworthy. In TABLE, the        Vo and Vo table compressor was free to compute dependency        relations in columns across all fields to rearrange data.        However, column data were too narrow to fully capture all        possible dependency relations. Again, the relational dependency        transforms computed by RDT had larger contexts to work with and        were more effective than TABLE at rearranging data for        compressibility.

FIG. 4 is a table 400 showing both compression and decompression timingresults. Here are some observations:

-   -   RDT was reasonably fast. Even a large file such as ihrwpxco with        more than 2 GBs of data was compressed in just 151 seconds on a        relatively slow processor. That was twice slower than Gzip but        the additional time taken was worth it given the compression        ratio improvement from under 12 to 1 to over 53 to 1.    -   Comparing RDT to FIELD and TABLE showed that the cost of        transforming data with relational dependency transforms was        acceptable, given the better compression ratios achievable. Even        on ca00003_uf1 with a large number of small fields where both        TABLE and RDT significantly slowed down, the time for RDT was        still reasonable.    -   Gzip was fastest as expected. However, Bzip was quite slow        because it used an algorithm for computing the Burrows-Wheeler        Transform that ran in quadratic time on data with highly        repetitive patterns. Such repetitions are common in relational        data due to fewer data values and frequent field correlations.

The performance of FIELD, TABLE and RDT as compared to Gzip and Bzipconfirmed that compressing relational data in a field-oriented way iseffective. Further, RDT did that well with relatively small time costs.

Discussion

The relational dependency transform discussed here generalized the1-transform used in the table compressor of Vo and Vo by lifting columndependency to field dependency. A key step was the introduction ofconditional compressive entropy as a way to measure the informationcontent in a field as well as across fields. The earlier comparison ofthe compressor RDT against FIELD and TABLE showed that the use of fielddependency could yield substantial improvement in both compression ratesand compression times over the use of just column dependency.

Raman and Swart discussed the use of field correlations to improvecompression by co-coding such fields. However, in their framework, thecorrelations must be specified manually. The RDT method described hereindiscovers field correlations automatically. In addition, depending onthe compressor used to compute compressive entropy, the computed fieldcorrelations could account for approximate matches in field values. Thatgives additional opportunities for enhancing compression.

Raman and Swart also discussed taking advantage of the lack of recordorder in a database table to sort records first to enhance compression.However, when records have many fields, it is difficult to tell what tosort by. And then, only some fields will be optimized while others not.The relational dependency transform discussed in the present disclosureaddresses that problem by sorting field values in an invertible waybased on dependency field transforms.

Certain information systems such as those based on the AT&T DaytonaDBMS, or the system storing the file stats compressed at an 80 to 1ratio with compressor RDT as described above, store database tables infiles and build indexes of records for fast access. As such, anycompressor used in these systems must preserve record order. Theseinformation systems also share a common data access pattern in whichdata are often written once but read many times. With disk transfer timeorders of magnitude slower than CPU time, compression could be acritical component in improving throughput. That is because wellcompressed data could be retrieved from disk much faster than raw dataand decompressed on line for processing. The mentioned informationsystem with the file stats indeed uses RDT and gains both reduced datastorage and fast data access.

Closely matched but different field data could sometimes indicateerrors. For example, going back to the running example relational datafile, the “Leno, J.” and “Leno, K.” values in its Name field could besuch erroneous instances instead of true distinct values since theircorresponding phone numbers were the same. That points to a way toidentify potential data quality issues using correlated fields. First,conditional compressive entropy could be used to compute pairs ofclosely correlated fields. Then, for each such pair of fields, anyvalues only approximately matched in one field but having exactlymatched correspondences in the other field could be flagged as potentialerrors.

The computation of an optimum dependency transform may be related to theautomatic discovery of field correlations. Limited experimentation hasshown that the transforms computed by method RDT tended to be stablewhen different ways to compute compressive entropy were used. Thathinted that such discovered dependency relations could be intrinsic tothe data, hence, reflecting the true ones as defined by data semantics.Given its efficiency, some variation of method RDT may be used todiscover relational structures in large files.

Implementation

The present disclosure may be implemented using hardware, firmware,software or any combination thereof, and may be implemented in one ormore computer systems and/or other processing systems. FIG. 5 is aschematic diagram of an exemplary computer system 500 that can be usedas a network access device or a server to implement the functionality ofthe present disclosure. It will be appreciated by those skilled in theart that computer system 500 may operate as a server that is networkedto other computers (network access devices) to operate as aclient/server system, as known by those skilled in the art, or computer500 may operate as a standalone system. Computer system 500 includes oneor more processors, such as processor 504. While a single processor 504is shown, the presently described linear programs may advantageously besolved using a multi-core machine. Processor 504 is connected to acommunication infrastructure 506 (e.g., a communications bus, cross-overbar, or network). Computer system 500 can include a display interface502 (e.g. a graphics card) that allows graphics, text, and other datafrom the communication infrastructure 506 (or from a frame buffer notshown) to be displayed on a display unit 530. Computer system 500 alsoincludes a main memory 508, preferably random access memory (RAM), andmay also include a secondary memory 510. The secondary memory 510 mayinclude, for example, a hard disk drive 512 and/or a removable storagedrive 514. The removable storage drive 514 has read/write functionalityonto removable storage media 518 having stored therein computer softwareand/or data. In alternative embodiments, secondary memory 510 mayinclude other similar devices for allowing computer programs or otherinstructions to be loaded into computer system 500. Such devices mayinclude, for example, a removable storage unit 522 and an interface 520.Examples of such may include a program cartridge and cartridge interface(such as that found in video game devices), a removable memory chip(such as an erasable programmable read only memory (EPROM), orprogrammable read only memory (PROM)) and associated socket, and otherremovable storage units 522 and interfaces 520, which allow software anddata to be transferred from the removable storage unit 522 to computersystem 500. Computer system 500 may also include a communicationsinterface 524 allowing software and data to be transferred betweencomputer system 500 and external devices. Examples of communicationsinterface 524 may include a modem, a network interface (such as anEthernet card), a communications port, a Personal Computer Memory CardInternational Association (PCMCIA) slot and card, etc. Software and datatransferred via communications interface 524 are in the form of signals(not shown), which may be electronic, electromagnetic, optical or othersignals capable of being received by communications interface 524. Thesesignals are provided to communications interface 524 via acommunications path (e.g., channel) 526. This path 526 carries thesignals and may be implemented using wire or cable, fiber optics, atelephone line, a cellular link, a radio frequency (RF) link and/orother communications channels. Computer programs (also referred to ascomputer control logic) are stored in main memory 508 and/or secondarymemory 510. Computer programs may also be received via communicationsinterface 524. Computer programs, when executed, enable the computersystem 500 to perform the features of the present disclosure, asdiscussed herein. Accordingly, such computer programs representcontrollers of the computer system 500. In an embodiment where thedisclosure is implemented using software, the software may be stored ina computer program product and loaded into computer system 500 usingremovable storage drive 514, hard drive 512, or communications interface524. The control logic (software), when executed by the processor 504,causes the processor 504 to perform the functions of the disclosure asdescribed herein. In another embodiment, the disclosure is implementedprimarily in hardware using, for example, hardware components, such asapplication specific integrated circuits (ASICs). Implementation of thehardware state machine so as to perform the functions described hereinwill be apparent to persons skilled in the relevant art(s). In oneexemplary embodiment, the system for the present disclosure may beimplemented as a desktop application program, which may reside on acomputer hard drive, database or other repository of data, or beuploaded from the Internet or other network (e.g., from a PC,mini-computer, mainframe computer, micro-computer, telephone device,PDA, or other network access device having a processor and input and/oroutput capability). Any available software tool capable of implementingthe concepts described herein may be used to implement the system andmethod of the present disclosure. The method and system of the presentdisclosure may also be implemented as an application-specific add-on toa program, or as a standalone application.

The above-described method may be implemented by program modules thatare executed by a computer, as described above. Generally, programmodules include routines, objects, components, data structures and thelike that perform particular tasks or implement particular abstract datatypes. The term “program” as used herein may connote a single programmodule or multiple program modules acting in concert. The disclosure maybe implemented on a variety of types of computers, including personalcomputers (PCs), hand-held devices, multi-processor systems,microprocessor-based programmable consumer electronics, network PCs,mini-computers, mainframe computers and the like. The disclosure mayalso be employed in distributed computing environments, where tasks areperformed by remote processing devices that are linked through acommunications network. In a distributed computing environment, modulesmay be located in both local and remote memory storage devices.

An exemplary processing module for implementing the methodology abovemay be hardwired or stored in a separate memory that is read into a mainmemory of a processor or a plurality of processors from a computerreadable medium such as a ROM or other type of hard magnetic drive,optical storage, tape or flash memory. In the case of a program storedin a memory media, execution of sequences of instructions in the modulecauses the processor to perform the process steps described herein. Theembodiments of the present disclosure are not limited to any specificcombination of hardware and software and the computer program coderequired to implement the foregoing can be developed by a person ofordinary skill in the art.

The term “computer-readable medium” as employed herein refers to anymachine encoded medium that provides or participates in providinginstructions to one or more processors. Such a medium includes but isnot limited to non-volatile media, volatile media and transmissionmedia. For example, non-volatile media can include optical or magneticmemory disks. Volatile media include dynamic random access memory(DRAM), which typically constitutes the main memory. Common expedientsof computer-readable media are well-known in the art and need not bedescribed in detail here.

CONCLUSION

The present disclosure considers the problem of compressing relationaldata files. Conditional compressive entropy was introduced as a measureof information in single fields and between fields relative to somegiven compressor. This entropy notion was then used to define optimumrelational dependency transforms suitable to condition relational datato make them more compressible. Efficient methods were presented tocompute such transforms, apply them to compress data and invert them todecompress.

Engineering aspects in using relational dependency transforms forcompression were discussed. Then, experimental results based on largedatasets from actual systems were presented to show the effectiveness ofthe approach. The use of relational dependency transforms forcompressing relational data file far outperformed standard tools such asGzip and Bzip2 at a reasonable time cost.

Last but not least, real world data files are not always uniform.Relational data files often contain extra information such as headersand comments or sometimes even multiple record types. Such specialstructures are too adhoc to classify. However, it is often simple torecode such data into better forms for processing by suitablecompression techniques. Thus, practical data compression requires notjust good algorithms but also good software methods that accommodatesuch ad-hoc data transformations. For example, a software frameworkcalled Vcodex (K.-P. Vo. The Vcodex Platform for Data Compression. InSoftware and Data Technologies, 2^(nd) Int. Conf, ICSOFT/ENASE (2007))may be used for writing data transforms and composing them forparticular compression tasks. The field and column dependency transformsdiscussed in the present disclosure as well as a large number of othergeneral compression algorithms may be included in such a framework.

The foregoing detailed description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the disclosure herein is not to be determined from the description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that variousmodifications will be implemented by those skilled in the art, withoutdeparting from the scope and spirit of the disclosure.

1. A method for preparing a relational database for compression by aparticular compressor, the method comprising: by a processor, computingan optimum relational dependency transform comprising a set of fielddependency relations each containing a predictor field of the relationaldatabase and a predictee field of the relational database, the computingcomprising computing an optimum branching of a first graph having a nodeset that is a set of possible predictor fields and predictee fields ofthe relational database, and having an edge set that comprises possibledependency relations between the predictor fields and the predicteefields, each edge having a weight based on a compression by theparticular compressor of a transform of the predictee field based on adefined permutation of the predictor field; by a processor, sorting thefields of the relational database topologically based on a second graphhaving a node set that is a set of all of the predictor fields and thepredictee fields of the optimum relational dependency transform, andhaving an edge set that comprises the set of field dependency relationsof the optimum relational dependency transform; by a processor, for eachpredictee field in a resulting topologically sorted relational database,transforming the predictee field based on the defined permutation of thepredictor field.
 2. The method of claim 1, wherein the particularcompressor is a data compressor tailored for compressing data of typesfound in the fields of relational database.
 3. The method of claim 1,wherein the defined permutation of the predictor field is based on a setof field-specific orderings of values.
 4. The method of claim 3, whereinthe values in the fields are ordered as strings of bytes and are sortedin a lexicographical order.
 5. The method of claim 3, wherein the valuesin the fields are ordered as numerical values and are sorted in anumerical order.
 6. The method of claim 3, wherein an applicationdefines its own ordering for the values in the fields.
 7. The method ofclaim 1, wherein there are no cyclic sequences in the optimum relationaldependency transform.
 8. A method for compressing a relational databaseusing a training set of records and a particular compressor, the methodcomprising: computing, by a processor, using the training set ofrecords, an optimum relational dependency transform comprising a set offield dependency relations each containing a predictor field of therelational database and a predictee field of the relational database,the computing comprising computing an optimum branching of a first graphhaving a node set that is a set of possible predictor fields andpredictee fields of the relational database, and having an edge set thatcomprises possible dependency relations between the predictor fields andthe predictee fields, each edge having a weight based on a compressionby the particular compressor of a transform of the predictee field basedon a defined permutation of the predictor field; producing atopologically sorted relational database by sorting, by a processor, thefields of the relational database topologically based on a second graphhaving a node set that is a set of all of the predictor fields and thepredictee fields of the optimum relational dependency transform, andhaving an edge set that comprises the set of field dependency relationsof the optimum relational dependency transform; for each predictee fieldin the topologically sorted relational database, transforming, by aprocessor, the predictee field based on the defined permutation of thepredictor field. dividing the topologically sorted relational databaseinto segments comprising groups of records; using the optimum relationaldependency transform, transforming the fields of each segment; andcompressing each transformed field using the predetermined compressor.9. The method of claim 8, wherein the predefined compressor is a datacompressor tailored for compressing data of types found in the fields ofrelational database.
 10. The method of claim 8, wherein the definedpermutation of the predictor field is based on a set of field-specificorderings of values.
 11. The method of claim 10, wherein the values inthe fields are ordered as strings of bytes and are sorted in alexicographical order.
 12. The method of claim 10, wherein the values inthe fields are ordered as numerical values and are sorted in a numericalorder.
 13. The method of claim 8, wherein there are no cyclic sequencesin the optimum relational dependency transform.
 14. The method of claim8, wherein an application defines its own ordering for the values in thefields.
 15. A tangible computer-usable medium having stored thereoncomputer readable instructions for compressing a relational databaseusing a training set of records and a particular compressor, whereinexecution of the computer readable instructions by a processor causesthe processor to perform operations comprising: computing, using thetraining set of records, an optimum relational dependency transformcomprising a set of field dependency relations each containing apredictor field of the relational database and a predictee field of therelational database, the computing comprising computing an optimumbranching of a first graph having a node set that is a set of possiblepredictor fields and predictee fields of the relational database, andhaving an edge set that comprises possible dependency relations betweenthe predictor fields and the predictee fields, each edge having a weightbased on a compression by the particular compressor of a transform ofthe predictee field based on a defined permutation of the predictorfield; producing a topologically sorted relational database by sortingthe fields of the relational database topologically based on a secondgraph having a node set that is a set of all of the predictor fields andthe predictee fields of the optimum relational dependency transform, andhaving an edge set that comprises the set of field dependency relationsof the optimum relational dependency transform; for each predictee fieldin the topologically sorted relational database, transforming thepredictee field based on the defined permutation of the predictor field.dividing the topologically sorted relational database into segmentscomprising groups of records; using the optimum relational dependencytransform, transforming the fields of each segment; and compressing eachtransformed field using the predetermined compressor.
 16. The tangiblecomputer-usable medium of claim 15, wherein the predefined compressor isa data compressor tailored for compressing data of types found in thefields of relational database.
 17. The tangible computer-usable mediumof claim 15, wherein the defined permutation of the predictor field isbased on a set of field-specific orderings of values.
 18. The tangiblecomputer-usable medium of claim 17, wherein the values in the fields areordered as strings of bytes and are sorted in a lexicographical order.19. The tangible computer-usable medium of claim 17, wherein the valuesin the fields are ordered as numerical values and are sorted in anumerical order.
 20. The tangible computer-usable medium of claim 15,wherein there are no cyclic sequences in the optimum relationaldependency transform.